If you have admin rights over the domain at your current registrar, you can usually transfer the domain easily. Make sure that the admin email address is correct in your domain record. If it is not, and you get stuck in the middle of the transfer, you may end up having to renew at your current registrar before you can transfer. Once a domain expires, you cannot transfer it without first renewing it - and if you renew and then transfer with 45 days, you can lose your renewal fee.
Once you are sure that the admin email information is correct, go to your new registrar and initiate a transfer request. You'll then need to confirm the transfer via email, your former registrar will have to confirm the transfer (can sometimes be painful, or even not possible!), and then the receiving registrar will have to approve the transfer. This can take hours or weeks, but generally takes a couple of days.
Don't wait until your domain is within only a few days of expiring to transfer it. You don't lose any time on your registration when you transfer, and your new registrar may need more than a few days to make it happen.